Andy Burnham has said his arrival in power will be a “circuit breaker” moment for Britain, pledging that his government will restore hope to millions of people, as he addressed the country for the first time from Downing Street.

After taking over from Keir Starmer, the new prime minister said he would set out a 10-year plan for the UK later this year to transform the UK from “where we are now to where I believe we all want Britain to be”.

Acknowledging the cost of living pressures across the country, he said he would start announcing measures on Tuesday to give them “some breathing space now”. He will begin making cabinet appointments on Monday afternoon, with Rachel Reeves and David Lammy already out.

After his speech, Burnham told reporters he was looking at cutting energy bills and bus fares as part of a fully funded cost of living support package that could eventually include more radical plans such as freezing private sector rents.

Andy Burnham pledges to address cost of living in first speech as UK PM - video

“We are looking at measures that could make a difference this year… We just want to do some things that people will feel and feel quite quickly,” he said. “It won’t solve everything, it won’t take all of the pressure off, but it just shows the direction of travel and that we’re serious about helping them out.”

In his speech, Burnham announced his first instruction in power would be to end rough sleeping, after a visit to homeless people in central London on Monday. He made a similar pledge when he became Greater Manchester mayor but oversaw four years of rising street homelessness.

Burnham formally took over from Starmer after meeting King Charles at Buckingham Palace, becoming the sixth UK prime minister in a decade, a speed of turnover which he acknowledged had resulted in may people becoming “fed up” with politics.

Speaking without notes, and watched by his wife, Marie-France van Heel, he said: “I am acutely conscious that I am the sixth person in the last 10 years to walk up this street, the seventh prime minister since 2016, making this a moment for reflection and new resolution.

Andy Burnham meets King Charles at Buckingham Palace. Photograph: Aaron Chown/PA

“It requires my generation of politicians to raise our game and rise to the new challenge. Britain needs to show the world that we can regain our stability once again, and that is our challenge to make politics work, to make it work better.

“I know people at home are fed up with politics. I hear you, and I want to be honest with you. We have not been good enough, and we need to be better. We will be.”

Burnham, who took over from Starmer as the leader of the Labour party on Friday, has put transforming the UK’s economic system at the heart of his plans, despite limited room for manoeuvre before the next election given his commitment to the fiscal rules.

“We will make this momenta circuit breaker for Britain, bringing forward the biggest changes in the last 40 years. A new political model and a new economic model,” he said.

Andy Burnham and his wife, Marie-France van Heel, outside No 10. Photograph: Kirsty Wigglesworth/AP

“In the 1980s, Britain took some wrong turns. Political power was centralised, economic power privatised, large parts of the country deindustrialised and they still haven’t recovered.

“Many feel as though they’re still in decline, and they don’t have the ability to turn things around. And that’s why we will change politics to make it more collaborative, more about problem solving than point scoring. And we will take power out of here and carry it into every postcode in the land, so that they can do more.”

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Speaking to reporters, Burnham said he would look at “any flexibility” within the government’s existing fiscal rules to help borrow billions more to invest in infrastructure – but that he would take a “very prudent” approach to the economy.

“I’ve said we’ll stick to the fiscal rules and by that I mean the existing fiscal rules and use obviously any flexibility within them. But we will stick to the existing rules,” he said. “So none of this is about taking risks with the economy. I’ve never done that in any role that I’ve had. I’ve always taken a very prudent approach.”

Burnham suggested he could cut income tax for lower earners in the budget. This could involve raising the tax-free personal allowance, which has been frozen for the last five years at £12,570 a year.

But the new prime minister refused to rule out bringing back the 50p top rate of tax – introduced by Gordon Brown’s government in 2010 – saying it was “premature” to make such decisions when he had just arrived at No 10.

“All of this will be looked at though at the budget, and obviously it’s difficult given the financial circumstances in which we find ourselves. But I wanted to recognise the point because it’s challenging for people and it’s people on the lowest incomes perhaps who’ve most been affected by that,” he said.

“So it’s an issue that I’m just kind of showing I have a visibility of the issue and the impact it’s had on the different groups that I’ve mentioned, but it’s difficult because changing the threshold is not without significant consequences. But I’m looking at it.”

Burnham said his government would put “the right values and the right standards” at its heart. “I will put the care of people at the heart of everything I do, I will give this my all, and I ask you all to pull with me,” he told the assembled crowd, which included his close ally Steve Rotheram, the Liverpool city region mayor, and the former Everton star Peter Reid.

“Let’s build a new national sense of unity, of common purpose, and positivity. Let us make this the moment when Britain starts to believe again, the moment we bring back hope.”